Investigation on supersymmetric Pauli-Villars regularization for supersymmetric standard models

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The generalized Pauli-Villars method proposed by Frolov and Slavnov suggests the possibility of chiral symmetric as well as gauge symmetric reguralization for chiral gauge theories and their supersymmetric extensions. By analyzing their method from general setting which is not specialized to a particular model, we reconstructed a generalized Pauli-Villlars regularization method, clarifying the validity of this method. We further tried to extend it to supersymmetric chiral gauge theories. The outcome of our investigation can be summarized as follows :1.The generalized Pauli-Villars method can be applied to theories with general gauge group. When fermions belong to an anomaly free representation, the theory can be reguralized without affecting both chiral and gauge symmetries. This result is highly nontrivial because it is generally believed that chiral symmetry can not be consistent with gauge symmetry in regularizing chiral fermions. For theories with anomalous fermion contents, this m … More ethod does not work completely and there arise singular terms in the gauge currents.2.The regularization yields automatically the transverse vacuum polarization tensor. Furthermore, the anomalies appearing in fermion numbers and conformal currents possess gauge invarinat forms.3.The generalized Pauli-Villars method turns out to be intimately related to Fujikawa's covariant regularization method since it preserves manifestly the gauge symmetry.4.A regularization which is manifestly gauge-covariant and supersymmetric can also be formulated for super-symmetric chiral gauge theories. It reproduces covariant gauge anomalies. It turned out that our method provids a simpler computational scheme for various anomalies.We have not succeeded in supersymmetrizing the generalized Pauli-Villars method, which should be investigated further. At present, it is not completely clear whether such generalization is possible or not. Our consequences obtained so far by analyzing the structure of covariantly regularized gauge currents strongly suggest the possibility of extending the generalized Pauli-Villars regularization to supersymmetric chiral gauge theories. Less